The unit circle approach to the construction of the sine and cosine functions and their inverses: An application of APOS theory

We use Action-Process-Object-Schema (APOS) Theory to analyze the mental constructions made by students in developing a unit circle approach to the sine, cosine, and their corresponding inverse trigonometric functions. Student understanding of the inverse trigonometric functions has not received much attention in the mathematics education research literature. We conjectured a small number of mental constructions, (genetic decomposition) which seem to play a key role in student understanding of these functions. To test and refine the conjecture we held semi-structured interviews with eleven students who had just completed a traditional college trigonometry course. A detailed analysis of the interviews shows that the conjecture is useful in describing student behavior in problem solving situations. Results suggest that students having a process conception of the conjectured mental constructions can perform better in problem solving activities. We report on some observed student mental constructions which were unexpected and can help improve our genetic decomposition.     

Commutative Group Algebras of Summable p-Groups

We study numerical semigroups generated by generalized arithmetic sequences. We present a membership criterion for such a numerical semigroup, and by this we are able to answer fundamental questions concerning a numerical semigroup such as computing the Frobenius number and the type of the numerical semigroup, and decide whether the numercial semigroup is symmetric. Also for this kind of numerical semigroups, we compute the cardinality of a minimal presentation and determine whether they are complete intersections.     

Unit Graphs Associated with Rings

Let R be a ring with nonzero identity. The unit graph of R, denoted by G(R), has its set of vertices equal to the set of all elements of R; distinct vertices x and y are adjacent if and only if x + y is a unit of R. In this article, the basic properties of G(R) are investigated and some characterization results regarding connectedness, chromatic index, diameter, girth, and planarity of G(R) are given. (These terms are defined in Definitions and Remarks 4.1, 5.1, 5.3, 5.9, and 5.13.)     

A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis

Data envelopment analysis (DEA) is a linear programming methodology to evaluate the relative technical efficiency for each member of a set of peer decision making units (DMUs) with multiple inputs and multiple outputs. It has been widely used to measure performance in many areas. A weakness of the traditional DEA model is that it cannot deal with negative input or output values. There have been many studies exploring this issue, and various approaches have been proposed.     

Influence of the structural properties on the pseudocritical magnetic behavior of single-wall ferromagnetic nanotubes

In this work we address the influence of the crystalline structure, concretely when the system under study is formed by square or hexagonal unit cells, upon the magnetic properties and pseudocritical behavior of single-wall ferromagnetic nanotubes. We focus not only on the effect of the geometrical shape of the unit cell but also on their dimensions. The model employed is based on the Monte Carlo method, the Metropolis dynamics and a nearest neighbors classical Heisenberg Hamiltonian. Magnetization per magnetic site, magnetic susceptibility, speci?c heat and magnetic energy were computed. These properties were computed varying the system size, unit cell dimension and temperature. The dependence of the nearest neighbor exchange integral on the nanotubes geometrical characteristics is also discussed. Results revealed a strong influence of the system topology on the magnetic properties caused by the difference in the coordination number between square and hexagonal unit cell. Moreover, the nanotubes diameter influence on magnetic properties is only observed at very low values, when the distance between atoms is less than it, presented by the 2D sheet. On the other hand, it was concluded that the surface-related finite-size effects do not influence the magnetic nanotubes properties, contrary to the case of other nano-systems as thin films and nanoparticles among others.     

Evaluation of a Statistically Equivalent Periodic Unit Cell for a quasi-periodic masonry

The paper presents a method to estimate the Statistically Equivalent Periodic Unit Cell (SEPUC) corresponding to a masonry with quasi-periodic texture. The identification of the texture and the constituent phases (unit blocks and mortar joints) is achieved by means of digital image processing techniques applied to color image of the masonry wall. A statistical analysis of geometrical parameters (width and height of blocks, thickness and length of mortar joints) allows to estimate their probability distribution and to identify the typology of the texture. Subsequently a Monte Carlo analysis is performed using several tentative SEPUCs generated with different dimensions of blocks and joints according to the estimated distributions. A criterion was eventually proposed to identify, among the numerically generated ones, the SEPUC which is more suitable to model the behavior of masonry wall. The SEPUC is analyzed with techniques available for periodic texture, applying periodic boundary conditions, in order to estimate the equivalent elastic stiffness. The proposed method is validated comparing the results in the elastic range obtained with SEPUC and those obtained imposing essential and natural boundary conditions on the original texture.     

Weighted-Hardy functions with Hadamard gaps on the unit ball

We prove that an analytic function f on the unit ball B with Hadamard gaps, that is, (the homogeneous polynomial expansion of f) satisfying n_k+1/n_k?λ>1 for all k∈N, belongs to the space if and only if . Moreover, we show that the following asymptotic relation holds . Also we prove that lim_r→1(1-r²)^α‖Rf_r‖_p=0 if and only if . These results confirm two conjectures from the following recent paper [S. Stevi?, On Bloch-type functions with Hadamard gaps, Abstr. Appl. Anal. 2007 (2007) 8 pages (Article ID 39176)].     

油田丛式抽油机井群集中控制系统的设计

为了解决油田抽油机采油效率和能耗较低等问题,本课题在抽油机单井变频节能控制技术的基础上,研发了丛式抽油机井群单井多模式柔性控制器,并建立丛式机井群一拖四的集中控制方案。通过选择合理的优化算法,实现了单井柔性控制与井组集中优化控制的有机结合,有针对性的提高了井群的整体能效。现场测试效果表明：该丛式抽油机柔性集中控制系统能够适应现场工况条件,实现抽油机井群系统的优化控制,并且能达到较好的控制效果与节能效果。     

大截面刚度CICC导体螺旋放送系统的设计与校核

聚变堆主机关键系统综合研究设施(CRAFT)是为了探索与建设中国聚变工程试验堆(CFETR)关键技术和原型系统的大科学装置.环向场(Toroidal Field, TF)线圈是CRAFT系统的重要组成部分,旨在制造出用于CFETR的环向场原型线圈.本文结合CRAFT TF线圈的结构特点和无张力绕制的工程需求,针对大截面刚度CICC导体恒速度、恒高度螺旋放送的技术难点,完成了导体放送系统的结构设计,并采用ANSYS软件对关键承载部件进行静力学校核,验证了导体放送系统结构设计的可靠性和材料选择的合理性.同时,对导体的螺旋放送过程进行简化,建立了待放导体旋转与下降过程的力学模型,获得了导体放送过程中克服转动惯量所需摩擦力的变化曲线,为导体安装撑紧力的设置提供了依据.     

Medium-term hydro-thermal coordination via hydro and thermal subsystem decomposition

Summary This paper addresses the medium-term hydro-thermal coordination problem in an electric energy system. That is, the problem of finding the energy production of every power plant (hydro or thermal) in every subperiod of a given planning period, so that the customer load is supplied at minimum cost. The planning horizon is typically one to two months and the first week of this planning period is modeled in detail. The solution method proposed decomposes the problem in two subproblems corresponding to the hydro and thermal subsystems. These two subproblems are coordinated using a coordinating function for every subperiod. The coordinating function of a given subperiod expresses total production cost in that subperiod as a function of the total hydro production in that subperiod. The decomposition proposed makes it possible to use specialized algorithms to solve the hydro and thermal subproblems. This results in a very efficient computational procedure. From an experimental point of view the coordinating mechanism is robust. A case study is provided. It considers 61 thermal plants, a hydro system including 8 cascaded hydro plants and a 48 subperiods planning period.